Symbolic systems for representing the world are fundamental to the way we understand some of the most basic domains of human experience, including time, number, and language. Understanding the contribution that these systems play in cognitive development requires cross-cultural research in which variations in symbol systems can be related to variations in the concepts children develop. Such research is of practical as well as theoretical importance because one of the main ways that cultures differ is in terms of the sets of symbolic tools they provide children. Symbolic systems may have very different effects on young children, who are trying to master symbolic tools at a time when they have little understanding of the domain those symbols describe, than they do on skilled adults using the same system. In predicting how symbol systems might affect cognition, therefore, it is useful to distinguish three kinds of effects that symbol systems might have: 1) effects on the initial acquisition of the system, 2) effects of the structure of symbolic system, once mastered, on information-processing using the system, and 3) effects that symbolic systems -may have in promoting or retarding conceptual understanding of the domains they represent. The proposed experiments fall into three sets -- 1) studies investigating how the structure of number, calendar, and language-representation systems affects the acquisition of these systems, 2) studies on the on-line computational effects such systems have on tasks such as calculating, reading, and performing calendar operations, and 3) studies of the conceptual consequences of using particular symbolic systems. For each of the domains of number, time, and written language, developmental comparisons between U.S. and Chinese children provide a promising method for understanding the role that symbolic structure plays in cognitive development. Understanding the developmental consequences of particular symbol systems is obviously important to determining how such cultural tools affect development; it is also essential to distinguishing general developmental problems that face children from obstacles that are contingent upon a culturally-specific way of organizing and representing bodies of knowledge.